# Suggested topics for a math DRP

Below is a list of suggested topics for your DRP project (courtesy of the University of Chicago math department's DRP program). These are only suggestions, and you are welcome to come up with others!

- algebra/combinatorics
- algebra/number theory
- algebraic curves
- algebraic curves and riemann surfaces
- algebraic geometry
- algebraic graph theory
- algebraic k-theory
- algebraic number theory
- algebraic topology
- algorithms of algebra and number theory
- analytic number theory
- applied mathematics
- bass-serre theory
- categorical logic
- category theory
- combinatorial game theory
- combinatorial topology
- combinatorics
- combinatorics/number theory
- commutative algebra and algebraic geometry
- compact lie groups
- complex algebraic curves
- complex algebraic geometry
- complex analysis
- complexity theory
- computability and algorithmic information
- diffential forms in algebraic topology
- differential geometry
- differential geometry and general relativity
- elementary number theory
- elliptic curves
- elliptic curves and cryptography
- ergodic theory in number theory
- euler characteristic and gauss-bonnet theorem
- existence and uniqueness for ordinary differential equations
- first-order logic and model theory
- flows on manifolds
- fourier analysis
- galois theory of differential equations
- game theory
- geometry and differential forms
- geometry of surfaces
- geometry/topology
- graph colorings
- grÃ¶bner bases
- group theory
- harmonic analysis
- homological algebra
- hyperbolic geometry
- introduction to characteristic classes
- introduction to logic
- introduction to manifolds
- introduction to probability
- knot theory
- lie groups
- lie groups and geometry
- linear algebra
- linear differential equations
- local class field theory via lubin-tate theory
- manifolds and lie groups
- mathematical physics
- matrix groups
- model theory
- models of peano arithmetic
- mordell's theorem
- nonstandard analysis
- number fields and class groups
- number theory
- number theory and combinatorics
- optimization theory
- p-adic analysis
- partial differential equations
- probability
- representation theory
- representation theory and quantum mechanics
- riemann surfaces
- riemann surfaces and elliptic curves
- sheaves, complex analysis and gaga
- special (co)limits and kan extensions
- stochastic processes
- the borsuk ulam theorem
- the fundamental group
- the prime number theorem
- the spectral theorem
- topoi and logic
- topological genericity
- topology from the differential viewpoint
- topology/analysis
- topos theory in physics
- tropical geometry
- van der waerden's theorem
- visual introduction to complex analysis
- young tableaux
- young tableaux and representations of the symmetric group
- zeta functions of number fields